1. Field of the Invention
This invention relates to a prediction filter that estimates a next sampled value from the sampled values that were sampled at the sampling frequency.
2. Description of the Prior Art
A conventional prediction filter is explained by referring to FIG. 2. FIG. 2 shows a configuration in the case of a first-degree prediction, in which a sampled value sampled at the sampling frequency is entered into the input terminal.
Designated 10, 11 are delay circuits that store sampled values and delay them by a sampling time interval T and output them to the next stage.
Designated 20, 21 are coefficient circuits that multiply the outputs of the delay circuits 10, 11 by a certain value and output the results.
Reference numeral 30 represents an adder that adds up the output values of the coefficient circuits 20, 21 to produce a prediction value.
The coefficients of the coefficient circuits 20, 21 have conventionally been determined as explained below.
Let sampled values at time t=T, 0, -T, -2T, . . . be y.sub.1, y.sub.0, y.sub.-1, y.sub.-2, . . . The prediction equation is given as EQU y=at+b (1)
Substituting y=y.sub.0 when t=0 into the equation (1), we obtain EQU y.sub.0 =b (2)
Substituting y=y.sub.-1 when t=-T into the equation (1) results in EQU y.sub.-1 =-aT+b (3)
Substituting the equation (2) into the equation (3) gives EQU aT=y.sub.0 -y.sub.-1 ( 4)
Thus, the prediction value&lt;y.sub.1 &gt; at t=T is obtained by substituting t=T into t. That is, EQU &lt;y.sub.1 &gt;=aT+b (5)
Substituting the equation (4) and (2) into the equation (5), we get EQU &lt;y.sub.1 &gt;=(y.sub.0 -y.sub.-1)+y.sub.0 =2y.sub.0 -y.sub.-1 ( 6)
That is, the sampled value y.sub.0 at t=0 is multiplied by 2 and the sampled value at t=-T is multiplied by -1 or inverted, and they are summed up to produce a prediction value&lt;y.sub.1 &gt;at t=T.
Therefore, the multiplication factor of the coefficient circuit 20 is set to 2 and that of the coefficient circuit 21 to -1.
When making prediction in the form of second-degree equation, the prediction equation is given by EQU y=at.sup.2 =bt+c (7)
y=y.sub.0 when t=0 is substituted in equation (7) to produce EQU y.sub.0 =c (8)
Substituting y=y.sub.-1 when t=-T into the equation (7), we obtain EQU y.sub.-1 =aT.sup.2 -bT+c (9)
Substituting y=y.sub.-2 when t=-2T into the equation (7) results in EQU y.sub.-2 =4aT.sup.2 -2bT+c (10)
From equation (8), (9) and (10), aT, bT and c are determined. EQU aT.sup.2 =(y.sub.2 -2y.sub.-1 +y.sub.0)/2 (11) EQU bT=(y.sub.-2 -4y.sub.-1 +3y.sub.0)/2 (12) EQU c=y.sub.0 ( 13)
The prediction value y1 at t=T is obtained as follows. t=T is substituted in equation (7) and we get EQU &lt;y.sub.1 &gt;=aT.sup.2 +bT+c (14)
Substituting the equation (11), (12) and (13) into equation (14) results in EQU &lt;y.sub.1 &gt;=3y.sub.0 -3y.sub.-1 +y.sub.-2 ( 15)
Therefore, in the case of prediction based on the second-degree equation, the configuration of the prediction filter in FIG. 2 is added with another stage of a delay circuit and a coefficient circuit, all stages connected to an adder, and the multiplication factors of the coefficient circuits are set, starting from the input side, to 3, -3 and 1.
In the above, we have described how the multiplication factors for the coefficient circuits based on the first-and second-degree equations are set. Similar setting is also done for the prediction based on the higher-degree equation.
In the conventional prediction filter, the coefficient circuit uses as a multiplication factor a coefficient determined as mentioned above.
As shown in FIG. 3, even when the input signal is superimposed with a signal component whose frequency is close to 1/2 the sampling frequency, we get EQU y.sub.0 =(y.sub.0)+.DELTA.y and EQU y.sub.-1 =(y.sub.-1)-.DELTA.y
and, as shown in equation (6), the prediction based on the first-degree equation is as follows. EQU &lt;y.sub.1 &gt;=2y.sub.0 -y.sub.-1 =2(y.sub.0)-(y.sub.-1)+3.DELTA.y (16)
The predicted value&lt;y.sub.1 &gt;, which is greatly different from the input signal value y.sub.1 (=2(y.sub.0)-y.sub.-1), is output from the adder 30.
In the case of the prediction based on a second-degree equation, the predicted value is given by equation (15). In this case also, the output predicted value is largely different from the input signal value.